1. Field of the Invention
Neural networks learn with the assistance of training data. In many areas of application, the training data are very noise-infested; for example, when modelling financial data such as stocks or currency rates. The training data thus contain random disturbances that have nothing to do with the system dynamics actually being modelled.
The transient structure of the random noise, however, also can be learned as a result of the approximation capability of the neural networks. This phenomenon is referred to as over-training of the neural network. The learning process of the neural network is considerably impeded in highly noise-infested systems due to an over-trained neural network since the generalization capability of the neural network is negatively influenced.
This problem is gaining in significance in areas of application wherein only a small plurality of training data vectors is available for the adaption of the neural network to the application; i.e., the function that is represented by the training data vectors and is to be modelled.
Particularly in these areas of application, but also generally in a training method of a neural network, it is advantageous to artificially generate additional training data vectors in order to obtain a larger training dataset.
2. Description of the Prior-Art
It is known to implement the generation of the artificial training vectors by infesting the available training data vectors of the training dataset with noise. In this context, it is known from document [1] to determine the training dataset with Gaussian noise having the average value 0 and a variance a that is set to the same value for all inputs of the neural network.
It is known from document [4] to generate training data by introducing additional noise. It is thereby known to utilize what is referred to as the jackknife procedure. This method, however, exhibits a number of disadvantages.
Indeed wherein a Gaussian noise with a variance that is set to the same value for all inputs of the neural network is employed for generating the additional training data vectors as statistical distribution that is used for generation, training data vectors are newly generated that contain no statement whatsoever about the system to be modelled. Further, the training data vectors contain no information whatsoever about the actual noise underlying the system. Although the training dataset is thus enlarged, this does not have to support the learning process since a permanently predetermined noise that has nothing to do with the actual system dynamics is employed for training the neural network. Over-training can then nonetheless arise.
Basics about neural networks are known, for example, from document [2]. Basics about employing neural networks in the economy are known, for example, from document [3].